Echo energy from a diffuse reflective target decays by spherical spreading. For a submerged target at depth d, and a ranging system at height h, above the surface, where h is greater than d, maximum working range, h, is controlled by the spherical spreading loss.
In the interaction of light with matter, the linearity of classical optics has always been regarded as a first approximation. Extensive experimental studies of non-linear optical effects became practical with the advent of lasers. By means of lasers highly monochromatic beams of great power, up to tens of thousands of megowatts, can now be obtained. The electromagnetic field of such beams are still considerably weaker than the intermolecular Coulomb fields, which are of the order of 10.sup.7 -10.sup.9 v/cm, but they are comparable to and sometimes stronger than, the fields that determine the probabilities of non-optical transitions and spontaneous emissions and causing splitting, shifts and broadening of the energy levels of transitions (intramolecular and magnetic intramolecular intereactions, and interactions with the vacuum electromagnetic field). It therefore becomes obvious that many spectral properties of molecules can be considerably altered by the action of intense laser light. These changes are not only responsible for the non-linear laws of propagation of intense light beams in matter (self-focusing, interaction of electromagnetic waves, and other effects) but they can also manifest themselves in the process of spontaneous emission (luminescence and scattering) and absorption of weak light from a separate source.
Light intensities required for satisfactory observation of the effects of radiation on the non-linear states and properties of molecules have been estimated to be on the order of 1MW/cm.sup.2. This is easily achieved. A criterion for this estimate was a relaxation time .tau. for the molecular populating levels, as determined by the probability of spontaneous emission and non-optical transitions, of .tau.&gt;&gt;10.sup.-9 SEC. For shorter relaxation times, in which molecules might accumulate, the population of the level will be non-linear at lower light intensities.
Laser beam energy densities much in excess of the threshold for non-linear effects and sufficient to bring about a liquid to vapor change of state in water, and by thermal shock to produce acoustic pulse rupture of the free liquid surface is commonplace knowledge.
Consider a medium with a square law propagation characteristic (i.e., input/output), A, for an incident light field E, or EQU A .alpha. E.sup.2 ( 1)
assume that the incident light consists of two monochromatic waves EQU E.sub.1 = E.sub.01 cos (.omega..sub.1 t - .phi..sub.1) EQU E.sub.2 = E.sub.02 cos (.omega..sub.2 t - .phi..sub.2) (2)
The substituting Equation (2) into Equation (1) results in the well known non-linear-combining spectral terms, that include four new frequency components, 2.sub..omega.1, 2.sub..omega.2, .omega..sub.1 + .omega..sub.2 and .omega..sub.1 - .omega..sub.2.